2023
Dynamic Optimization
Name: Dynamic Optimization
Code: MAT13506L
6 ECTS
Duration: 15 weeks/156 hours
Scientific Area:
Mathematics
Teaching languages: Portuguese
Languages of tutoring support: Portuguese, English
Regime de Frequência: Presencial
Sustainable Development Goals
Learning Goals
The objective of this course is the basic training in theory of optimization of dynamic systems, with a view to the future development, either of the knowledge in this area, as well as its use in other areas of Mathematics or Economics and Management.
At the end of u.c. It is intended that the student learns:
- formulate optimal control models and dynamic programming in various contexts in the areas of Economics, Management, Engineering, Biology;
- know the main methods of solving these problems.
In addition, it is intended to develop:
- students' abstract thinking to solve, more simply and more generally, concrete problems
- capacity for abstraction, creative intuition, model building and critical thinking.
At the end of u.c. It is intended that the student learns:
- formulate optimal control models and dynamic programming in various contexts in the areas of Economics, Management, Engineering, Biology;
- know the main methods of solving these problems.
In addition, it is intended to develop:
- students' abstract thinking to solve, more simply and more generally, concrete problems
- capacity for abstraction, creative intuition, model building and critical thinking.
Contents
Optimization of dynamic systems and processes, control problems. Historical introduction.
Calculation of variations. Important particular examples: geodetic, brachistochrone problem, revolution surfaces of minimal area. Euler's equation. Condition of transversality.
Control theory. Controllability. Optimal control problems. Examples in Economics and Management. Pontryagin's maximum principle. Model of optimal economic growth. Control problem in discrete time.
Dynamic programming. Multistage decision processes. Bellman's principle of optimality. Typical problems of dynamic programming.
Calculation of variations. Important particular examples: geodetic, brachistochrone problem, revolution surfaces of minimal area. Euler's equation. Condition of transversality.
Control theory. Controllability. Optimal control problems. Examples in Economics and Management. Pontryagin's maximum principle. Model of optimal economic growth. Control problem in discrete time.
Dynamic programming. Multistage decision processes. Bellman's principle of optimality. Typical problems of dynamic programming.
Teaching Methods
Teaching methodologies: Structured exposition, examples with emphasis on applications and on solving exercises. To stimulate students initiative, so that classes become essentially centered on students activities, guided by their teacher; instead of on teachers activities, copied by students. Particularly in what concerns submission of questions and/or suggestions of application and/or description of contents, the solving of exercises, participation in discussions, etc.
Evaluation: One written test and one written work elaborated by the student individually or in a small group (the final mark is its average, students are exempted from final examination if the average is greather or equal to 10/20, with minimal approval grade of 8/20 in the written test); or else one written exam, with one possibility to repeat the exam later.
Evaluation: One written test and one written work elaborated by the student individually or in a small group (the final mark is its average, students are exempted from final examination if the average is greather or equal to 10/20, with minimal approval grade of 8/20 in the written test); or else one written exam, with one possibility to repeat the exam later.
Teaching Staff
- Luís Miguel Zorro Bandeira [responsible]
